Solve 20x^270x^550x^3

$$20 x ^ { 2 } 70 x ^ { 5 } 50 x ^ { 3 }$$

Evaluate

$$70000x^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$20x^{7}\times 70\times 50x^{3}$$

To multiply powers of the same base, add their exponents. Add 7 and 3 to get 10.

$$20x^{10}\times 70\times 50$$

Multiply 20 and 70 to get 1400.

$$1400x^{10}\times 50$$

Multiply 1400 and 50 to get 70000.

$$70000x^{10}$$

Differentiate w.r.t. x

$$700000x^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(20x^{7}\times 70\times 50x^{3})$$

To multiply powers of the same base, add their exponents. Add 7 and 3 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(20x^{10}\times 70\times 50)$$

Multiply 20 and 70 to get 1400.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1400x^{10}\times 50)$$

Multiply 1400 and 50 to get 70000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(70000x^{10})$$

The derivative of ax^{n} is nax^{n-1}.

$$10\times 70000x^{10-1}$$

Multiply 10 times 70000.

$$700000x^{10-1}$$

Subtract 1 from 10.

$$700000x^{9}$$